This application relates to analog computation using numerical representations with uncertainty, for example, as represented by soft bytes.
Statistical inference can involve manipulation of quantities that represent uncertainty in numerical values. Statistical inference can make use of statistics to draw inferences based on incomplete or inaccurate information. Statistical inference problems can be found in many application areas—from opinion polling to medical research to telecommunications systems. The field of statistical inference encompasses a wide variety of techniques for performing this task.
In some applications, statistical inference problems involve extracting information from a measurement of data that has been corrupted in some way. For example, a wireless receiver typically receives one or more radio signals that have been corrupted by noise, interference, and/or reflections. Statistical inference techniques can be used to attempt to extract the original transmitted information from the corrupted signal that was received.
In statistical inference, the language of probability is often used to quantitatively describe the likelihood that a particular condition is true. The meaning of these probabilities can be interpreted in different ways, although these interpretations are sometimes interchangeable. For example, very generally, a probability can be interpreted either as the degree of confidence that a condition is true, or alternatively as the fraction of times the condition will be true among a large number of identical experiments. Probabilities can be represented in the linear domain, for example, as real numbers from 0 to 1, where 1 is interpreted as complete confidence that the condition is true, and 0 is interpreted as complete confident that the condition will not occur. Probabilities can also be represented in the logarithmic domain, for example, using log likelihood ratios (or LLRs) representing the log of the ratio of the linear probabilities (the log odds). In some examples, the LLR of a binary variable x is defined as the logarithm of the ratio of the probability of x being 1 and the probability of x being 0, i.e.,
      LLR    ⁡          (      x      )        =            log      ⁡              (                              p            ⁡                          (                              x                =                1                            )                                            p            ⁡                          (                              x                =                0                            )                                      )              .  In LLR representations, complete certainty of a condition being true is represented by +∞, complete certainty of a condition being false is represented by −∞, and complete uncertainty is represented by a value of 0.
Examples of techniques for solving statistical inference problems or for generating approximate solutions to statistical inference problems include belief propagation, which exploits the dependency (or the lack of dependency) between variables that can be translated into network elements. Some forms of belief propagation operate by passing messages between nodes in a factor graph that represents the system model, where each message represents a summary of the information known by that node through its connections to other nodes.